Characterizing permeability-porosity relationships of porous rocks using a stress sensitivity model in consideration of elastic-structural deformation and tortuosity sensitivity

Abstract

Clarifying the relationship between stress sensitivities of permeability and porosity is of great significance in guiding underground resource mining. More and more studies focus on how to construct stress sensitivity models to describe the relationship and obtain a comprehensive stress sensitivity of porous rock. However, the limitations of elastic deformation calculation and incompleteness of considered tortuosity sensitivity lead to the fact that the existing stress sensitivity models are still unsatisfactory in terms of accuracy and generalization. Therefore, a more accurate and generic stress sensitivity model considering elastic-structural deformation of capillary cross-section and tortuosity sensitivity is proposed in this paper. The elastic deformation is derived from the fractal scaling model and Hooke's law. Considering the effects of elastic-structural deformation on tortuosity sensitivity, an empirical formula is proposed, and the conditions for its applicability are clarified. The predictive performance of the proposed model for the permeability-porosity relationships is validated in several sets of publicly available experimental data. These experimental data are from different rocks under different pressure cycles. The mean and standard deviation of relative errors of predicted stress sensitivity with respect to experimental data are 2.63% and 1.91%. Compared with other models, the proposed model has higher accuracy and better predictive generalization performance. It is also found that the porosity sensitivity exponent α, which can describe permeability-porosity relationships, is 2 when only elastic deformation is considered. α decreases from 2 when structural deformation is also considered. In addition, α may be greater than 3 due to the increase in tortuosity sensitivity when tortuosity sensitivity is considered even if the rock is not fractured.